Description

• Title:
  Homoclinic solutions for a class of autonomous second order Hamiltonian systems with a superquadratic potential
• Creator:
  Janczewska, Joanna
• Description:
  We will prove the existence of a nontrivial homoclinic solution for an autonomous second order Hamiltonian system $\ddot{q}+\nabla{V}(q)=0$, where $q\in\mathbb{R}^n$, a potential $V\colon\mathbb{R}^n\to\mathbb{R}$ is of the form $V(q)=-K(q)+W(q)$, $K$ and $W$ are $C^{1}$-maps, $K$ satisfies the pinching condition, $W$ grows at a superquadratic rate, as $|q|\to\infty$ and $W(q)=o(|q|^2)$, as $|q|\to 0$. A homoclinic solution will be obtained as a weak limit in the Sobolev space $W^{1,2}(\mathbb{R},\mathbb{R}^n)$ of a sequence of almost critical points of the corresponding action functional. Before passing to a weak limit with a sequence of almost critical points each element of this sequence has to be appropriately shifted.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2010.04.23
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 36, No 1 (September 2010); 19 - 26;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2010.025/8448
• Subject:
  Action functional;
  Hamiltonian system;
  homoclinic solution;
  general minimax principle;
  superquadratic potential;
  37J45;
  58E05;
  34C37;
  70H05
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2010.025
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other